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Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete…
Music is an art, perceived in unique ways by every listener, coming from acoustic signals. In the meantime, standards as musical scores exist to describe it. Even if humans can make this transcription, it is costly in terms of time and…
We study classes of musical scales obtained from shift spaces in symbolic dynamics through the first symbol rule, which yields scales in any $n$-TET tuning system. The modes are thought as elements of orbit equivalence classes of cyclic…
For example, in the chromatic circle, the twelve tones are represented by twelve points on a circle, and in Tonnetz, the relationships among harmonies are represented by a triangular lattice. Recently, we have shown that several…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
This article concerns a generalization of the Temperley-Lieb algebra, important in applications to conformal field theory. We call this algebra the valenced Temperley-Lieb algebra. We prove salient facts concerning this algebra and its…
The procedure underlying the matching of 1-form (tetrad) fields in theories possessing absolute parallelism -- f(T) gravity being within this category -- is addressed and exemplified. We show that the remnant symmetries of the intervening…
Musical intervals in multiple of semitones under 12-note equal temperament, or more specifically pitch-class subsets of assigned cardinality ($n$-chords) are conceived as positive integer points within an Euclidean $n$-space. The number of…
We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…
Formulating a rigorous system-bath partitioning approach remains an open issue. In this context the famous Caldeira-Leggett model that enables quantum and classical treatment of Brownian motion on equal footing has enjoyed popularity.…
Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth…
Musical audio is generally composed of three physical properties: frequency, time and magnitude. Interestingly, human auditory periphery also provides neural codes for each of these dimensions to perceive music. Inspired by these intrinsic…
In our previous papers, we have introduced within the theory of the Riemann zeta function the following notions: Jacob's ladders, oscillating systems, $\zeta$-factorization, metamorphoses, \dots In this paper we obtain $\zeta$-analogue of…
There is a wide variety of music similarity detection algorithms, while discussions about music plagiarism in the real world are often based on audience perceptions. Therefore, we aim to conduct a study to examine the key criteria of human…
We have experimentally observed re-equilibration of a magnetically trapped cloud of metastable neon atoms after it was put in a non-equilibrium state. Using numerical simulations we show that anharmonic mixing, equilibration due to the…
Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…
This study borrows and extends probabilistic language models from natural language processing to discover the syntactic properties of tonal harmony. Language models come in many shapes and sizes, but their central purpose is always the…
We consider tensor data completion of an incomplete observation of multidimensional harmonic (MH) signals. Unlike existing tensor-based techniques for MH retrieval (MHR), which mostly adopt the canonical polyadic decomposition (CPD) to…
We report on a result on quantum electrodynamics on a three dimensional Euclidean spacetime. The model is formulated on a toroidal lattice with unit volume and variable lattice spacing. The result is that the renormalized partition function…
We propose a timbre conversion model based on the Diffusion architecture de-signed to precisely translate music played by various instruments into piano ver-sions. The model employs a Pitch Encoder and Loudness Encoder to extract pitch and…